solve_QP_SOCP: Solve a Quadratic Programming Problem

In DWD: DWD implementation based on A IPM SOCP solver

Description

This routine implements the second order cone programming method from Kim-Chuan Toh , Michael J. Todd, and Reha H. Tutuncu for solving quadratic programming problems of the form min(-d^T b + 1/2 b^T D b) with the constraints A^T b >= b_0.

Usage

solve_QP_SOCP(Dmat, dvec, Amat, bvec)

Arguments

Dmat	matrix appearing in the quadratic function to be minimized.
dvec	vector appearing in the quadratic function to be minimized.
Amat	matrix defining the constraints under which we want to minimize the quadratic function.
bvec	vector holding the values of b_0 (defaults to zero).

Value

a list with the following components:

solution

vector containing the solution of the quadratic programming problem.

Author(s)

Hanwen Huang: [e-mail]; Perry Haaland: [e-mail]; Xiaosun Lu: [e-mail]; Frances Tong: [e-mail]; Elaine McVey: [e-mail]; Yufeng Liu: [e-mail]; J. S. Marron: [e-mail]

References

Kim-Chuan Toh , Michael J. Todd, and Reha H. Tutuncu
SDPT3 version 4.0 – a MATLAB software for semidefinite-quadratic-linear programming
http://www.math.nus.edu.sg/~mattohkc/sdpt3.html

See Also

sqlp

Examples

##
## Assume we want to minimize: -(0 5 0) %*% b + 1/2 b^T b
## under the constraints:      A^T b >= b0
## with b0 = (-8,2,0)^T
## and      (-4  2  0)
##      A = (-3  1 -2)
##          ( 0  0  1)
## we can use solve.QP as follows:
##
Dmat       <- matrix(0,3,3)
diag(Dmat) <- 1
dvec       <- c(0,5,0)
Amat       <- matrix(c(-4,-3,0,2,1,0,0,-2,1),3,3)
bvec       <- c(-8,2,0)
solve_QP_SOCP(Dmat,dvec,Amat,bvec=bvec)

Example output

Loading required package: Matrix
$solution
          [,1]
[1,] 0.4760164
[2,] 1.0479825
[3,] 2.0959526

There were 12 warnings (use warnings() to see them)

DWD documentation built on May 2, 2019, 5 p.m.